So you've finished your Tier 1 and 2 Islands on your main, had bad luck, or working on your alts, and getting to item level 600 is just out of reach. What are you supposed to do about that? Wait another few days doing Chaos dungeons? There are a few different tricks you can do to progress through.
I'm going to assume you have finished your tier 1 islands. You're either working on an alt or had very bad luck upgrading your gear. Item level 550-600 can be a huge pain. For me, I am usually running out of the armor/weapon stones, but near this item range, it's actually the harmony shards that are a pain. On my server at the time of writing 1000 harmony shards on the auction house is roughly 500g. I need ~3k harmony stones per level on each piece of gear.
If you are doing this on an alt AND have your main in your 802 tier 2 gear. Please use your Stronghold to do research. That will reduce the materials needed to hone, and increase the chances of success.
The easiest method is to do your dungeons in Rohendel on hard mode. Each of those Dungeons will give you some extra Harmony Shards. If you did them on the hard mode the first time then do them on normal mode. You need these for adventure journal anyways. Normal mode will give you some Guardian/Destruction stones. There are two different dungeons you can do this with on Rohendel. This info also applies to Tier 2 dungeons as well.
The other easiest option is to complete the Shadowspire/Fatespire. You can queue for this from most of the major towns. You'll want to complete Shadowspire/Fatespire on your main first. This gets rid of a lot of the non-upgrade material rewards. Then when your alts go through them you'll get more materials in place of those other rewards.
Do your Abyssal Dungeons! It's generally worth doing the bonus roll for gold at the end of the dungeon. You'll still have a net profit of gold even before selling books. These dungeons will give you additional materials, and even better a chance at a legendary card for your collection.